import numpy as np
import matplotlib.pyplot as plt
import scipy.special as sp

col = ['orange', 'purple', 'deepskyblue', 'mediumseagreen']

X = np.arange(-5, 5, 0.01)

plt.clf()
plt.figure(figsize=(4,3.2))
plt.axes([0.14,0.12,0.83,0.82])

X = np.arange(-5, 5, 0.01)

A = []
for k,(x,g) in enumerate([(0,0.5),(0,1),(0,2),(-2,1)]):
    Y = np.arctan((X-x)/g)/np.pi + 0.5
    a = plt.plot(X, Y, '-', color=col[k], lw=1.7)
    A.append(a)

plt.xlabel("$x$")
plt.ylabel(r"$P(X\le x)$")
plt.ylim([0,1.0])
plt.tick_params(direction='in', top=True, right=True)

plt.legend(("$x_0=0,\\, \\gamma=0.5$", "$x_0=0,\\,\\gamma=1$",\
                    "$x_0=0,\\, \\gamma=2$", "$x_0=-2,\\, \\gamma=1$"),
                numpoints=1, handlelength=0.75, handletextpad=0.5,\
                loc="lower right", frameon=False)

plt.xlim(-5,5)

plt.savefig("cauchy_cdf.pdf")
plt.savefig("cauchy_cdf.svg")